d <- read_sav(here("data", "d4 - scales & covariates.sav"))

Model assumptions & diagnostics

Normality assumption: outcome

d$engage

##  [1] 4.500 4.250 4.375 3.875 4.875 3.875 3.625 4.000 4.750 4.375 3.250 4.375
## [13] 3.875 3.625 3.500 3.875 3.875 3.625 3.750 3.750 4.375 4.500 4.500 3.875
## [25] 4.875 4.250 4.875 3.875 4.625 4.625 4.000 3.250 5.000 4.000 4.000 4.125
## [37] 4.125 4.500 4.000 4.500 3.500 5.000 3.625 3.875 3.875 4.250 3.625 4.750
## [49] 4.750 3.000 4.625 4.250 3.625 4.750 5.000 3.750 4.750 4.250 4.000 4.750
## [61] 4.250 3.375 4.875 3.750 4.500 4.625 4.000 3.875 3.625 4.750 4.250 4.625
## [73] 3.125 4.625 3.000 4.375 4.000 4.375 3.500 3.000 2.250 4.500 4.000 3.750
## [85] 4.500 4.750 3.375 4.125 4.500 3.750 4.000 3.250 3.500 4.500
## attr(,"format.spss")
## [1] "F8.2"

ggplot(d, aes(engage)) +
geom_histogram(alpha = 0.7) # meets normality assumption? assumption may be tenable, maybe presence of an outlier (score 2.250) participant row 81

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

d_no81 <- d %>%
  filter(participant_id != "608_1") # 93 rows now

ggplot(d_no81, aes(engage)) +
  geom_histogram(alpha = 0.7)

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Academic approach (tutor)

linearity

ggplot(d, aes(hwi_1, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## `geom_smooth()` using formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## Warning: Removed 1 rows containing missing values (geom_point).

ggplot(d_no81, aes(hwi_1, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## `geom_smooth()` using formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).
## Removed 1 rows containing missing values (geom_point).

# plots - univariate

m_hwi_1a <- lm(engage ~ hwi_1, d)
plot(m_hwi_1a)

m_hwi_1a_d_no81 <- lm(engage ~ hwi_1, d_no81)
plot(m_hwi_1a_d_no81)

coef(m_hwi_1a)

## (Intercept)       hwi_1 
##   3.6873295   0.1519164

coef(m_hwi_1a_d_no81)

## (Intercept)       hwi_1 
##  3.89924713  0.08042387

outliers

plot(m_hwi_1a, which = 4)

plot(m_hwi_1a_d_no81, which = 4)

structuring/monitoring approach to HWI

linearity

ggplot(d, aes(hwi_2, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## `geom_smooth()` using formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## Warning: Removed 1 rows containing missing values (geom_point).

ggplot(d_no81, aes(hwi_2, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## `geom_smooth()` using formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).
## Removed 1 rows containing missing values (geom_point).

# plots

m_hwi_2a <- lm(engage ~ hwi_2, d)
plot(m_hwi_2a)

m_hwi_2a_d_no81 <- lm(engage ~ hwi_2, d_no81)
plot(m_hwi_2a_d_no81)

coef(m_hwi_2a)

## (Intercept)       hwi_2 
##   3.3847767   0.2188261

coef(m_hwi_2a_d_no81)

## (Intercept)       hwi_2 
##   3.6388939   0.1461771

outliers

plot(m_hwi_2a, which = 4)

plot(m_hwi_2a_d_no81, which = 4)

positive reinforcement to increase HW completion

linearity

ggplot(d, aes(hwi_3, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## `geom_smooth()` using formula 'y ~ x'

## Warning: Removed 1 rows containing non-finite values (stat_smooth).

## Warning: Removed 1 rows containing missing values (geom_point).

# plots

m_hwi_3a <- lm(engage ~ hwi_3, d)
plot(m_hwi_3a)

m_hwi_3a_d_no81 <- lm(engage ~ hwi_3, d_no81)
plot(m_hwi_3a_d_no81)

coef(m_hwi_3a)

## (Intercept)       hwi_3 
##   3.6791139   0.1524149

coef(m_hwi_3a_d_no81)

## (Intercept)       hwi_3 
##   3.8346718   0.1024288

outliers

plot(m_hwi_3a, which = 4)

plot(m_hwi_3a_d_no81, which = 4)

monitoring

linearity

ggplot(d, aes(monit, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

plots

m_monit_a <- lm(engage ~ monit, d)
plot(m_monit_a)

m_monit_a_no81 <- lm(engage ~ monit, d_no81)
plot(m_monit_a_no81)

coef(m_monit_a)

## (Intercept)       monit 
##  4.03395459  0.02047014

coef(m_monit_a_no81)

## (Intercept)       monit 
##    4.452410   -0.108462

outliers

plot(m_monit_a, which = 4)

plot(m_monit_a_no81, which = 4)

5. structure at home

linearity

ggplot(d, aes(str_home, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

# plots

m_str_home_a <- lm(engage ~ str_home, d)
plot(m_str_home_a)

m_str_home_a_no81 <- lm(engage ~ str_home, d_no81)
plot(m_str_home_a_no81)

coef(m_str_home_a)

## (Intercept)    str_home 
##   3.3138044   0.2662147

coef(m_str_home_a_no81)

## (Intercept)    str_home 
##   3.7137830   0.1363654

outliers

plot(m_str_home_a, which = 4)

plot(m_str_home_a_no81, which = 4)

6. convos: child beh & school climate

linearity

ggplot(d, aes(convos_1, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

plots

m_convos_1a <- lm(engage ~ convos_1, d)
plot(m_convos_1a)

m_convos_1a_no81 <- lm(engage ~ convos_1, d_no81)
plot(m_convos_1a_no81)

coef(m_convos_1a)

## (Intercept)    convos_1 
##  4.15626415 -0.01673332

coef(m_convos_1a_no81)

## (Intercept)    convos_1 
##  4.18311182 -0.01870638

outliers

plot(m_convos_1a, which = 4)

plot(m_convos_1a_no81, which = 4)

7. convos: future career planning

linearity

ggplot(d, aes(convos_2, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

# plots

m_convos_2a <- lm(engage ~ convos_2, d)
plot(m_convos_2a)

m_convos_2a_no81 <- lm(engage ~ convos_2, d_no81)
plot(m_convos_2a_no81)

coef(m_convos_2a)

## (Intercept)    convos_2 
##   3.6189155   0.1489131

coef(m_convos_2a_no81)

## (Intercept)    convos_2 
##   3.5987248   0.1615428

outliers

plot(m_convos_2a, which = 4)

plot(m_convos_2a_no81, which = 4)

convos: child’s social involvement # linearity

ggplot(d, aes(convos_3, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

plots

m_convos_3a <- lm(engage ~ convos_3, d)
plot(m_convos_3a)

m_convos_3a_no81 <- lm(engage ~ convos_3, d_no81)
plot(m_convos_3a_no81)

coef(m_convos_3a)

## (Intercept)    convos_3 
##   3.7249928   0.1074522

coef(m_convos_3a_no81)

## (Intercept)    convos_3 
##  3.78682533  0.09526841

outliers

plot(m_convos_3a, which = 4)

plot(m_convos_3a_no81, which = 4)

9. Basic involvement # linearity

ggplot(d, aes(sbi_1, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

plots

m_sbi_1a <- lm(engage ~ sbi_1, d)
plot(m_sbi_1a)

m_sbi_1a_no81 <- lm(engage ~ sbi_1, d_no81)
plot(m_sbi_1a_no81)

coef(m_sbi_1a)

## (Intercept)       sbi_1 
##   3.4600308   0.2160509

coef(m_sbi_1a_no81)

## (Intercept)       sbi_1 
##   3.6681932   0.1516645

outliers

plot(m_sbi_1a, which = 4)

plot(m_sbi_1a_no81, which = 4)

10. Resource-intensive involvement # linearity

ggplot(d, aes(sbi_2, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

plots

m_sbi_2a <- lm(engage ~ sbi_2, d)
plot(m_sbi_2a)

m_sbi_2a_no81 <- lm(engage ~ sbi_2, d_no81)
plot(m_sbi_2a_no81)

coef(m_sbi_2a)

## (Intercept)       sbi_2 
##   3.4730366   0.2364352

coef(m_sbi_2a_no81)

## (Intercept)       sbi_2 
##   3.7845217   0.1251092

outliers

plot(m_sbi_2a, which = 4)

plot(m_sbi_2a_no81, which = 4)

11. Belongingness # linearity

ggplot(d, aes(belong, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

# plots

m_belong_a <- lm(engage ~ belong, d)
plot(m_belong_a)

m_belong_a_no81 <- lm(engage ~ belong, d_no81)
plot(m_belong_a_no81)

coef(m_belong_a)

## (Intercept)      belong 
## 4.079666022 0.005713666

coef(m_belong_a_no81)

## (Intercept)      belong 
##  4.21013216 -0.03056167

outliers

plot(m_belong_a, which = 4)

plot(m_belong_a_no81, which = 4)

Endorsemnt # linearity

ggplot(d, aes(endorse, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : pseudoinverse used at 3

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : neighborhood radius 0.33333

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : reciprocal condition number 0

## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : pseudoinverse used at 3

## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : neighborhood radius
## 0.33333

## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : reciprocal condition
## number 0

## `geom_smooth()` using formula 'y ~ x'

# plots

m_endorse_a <- lm(engage ~ endorse, d)
plot(m_endorse_a)

m_endorse_a_no81 <- lm(engage ~ endorse, d_no81)
plot(m_endorse_a_no81)

coef(m_endorse_a)

## (Intercept)     endorse 
##  4.37416770 -0.08779808

coef(m_endorse_a_no81)

## (Intercept)     endorse 
##   4.4549694  -0.1070505

outliers

plot(m_endorse_a, which = 4)

plot(m_endorse_a_no81, which = 4)

Value & supp of Ed # linearity

ggplot(d, aes(value_ed, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

plots

m_value_ed_a <- lm(engage ~ value_ed, d)
plot(m_value_ed_a)

m_value_ed_a_no81 <- lm(engage ~ value_ed, d_no81)
plot(m_value_ed_a_no81)

coef(m_value_ed_a)

## (Intercept)    value_ed 
##  3.96306916  0.03809425

coef(m_value_ed_a_no81)

## (Intercept)    value_ed 
##   3.7935313   0.0920712

outliers

plot(m_value_ed_a, which = 4)

plot(m_value_ed_a_no81, which = 4)

Rel with teachers: comfort, interest, and openness # linearity

ggplot(d, aes(rel_1, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

# plots

m_rel_1a <- lm(engage ~ rel_1, d)
plot(m_rel_1a)

m_rel_1a_no81 <- lm(engage ~ rel_1, d_no81)
plot(m_rel_1a_no81)

coef(m_rel_1a)

## (Intercept)       rel_1 
##    4.683435   -0.187491

coef(m_rel_1a_no81)

## (Intercept)       rel_1 
##  4.40937847 -0.09375073

outliers

plot(m_rel_1a, which = 4)

plot(m_rel_1a_no81, which = 4)

Rel with school: parent self-efficacy to solve probs with school # linearity

ggplot(d, aes(rel_2, engage)) +
geom_point() +
geom_smooth() +
geom_smooth(method = "lm",
color = "magenta")

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : pseudoinverse used at 3

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : neighborhood radius 0.25

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : reciprocal condition number 0

## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : pseudoinverse used at 3

## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : neighborhood radius 0.25

## Warning in predLoess(object$y, object$x, newx = if
## (is.null(newdata)) object$x else if (is.data.frame(newdata))
## as.matrix(model.frame(delete.response(terms(object)), : reciprocal condition
## number 0

## `geom_smooth()` using formula 'y ~ x'

plots

m_rel_2a <- lm(engage ~ rel_2, d)
plot(m_rel_2a)

m_rel_2a_no81 <- lm(engage ~ rel_2, d_no81)
plot(m_rel_2a_no81)

coef(m_rel_2a)

## (Intercept)       rel_2 
##  3.90116608  0.06351959

coef(m_rel_2a_no81)

## (Intercept)       rel_2 
##  4.25640514 -0.04508926

outliers

plot(m_rel_2a, which = 4)

plot(m_rel_2a_no81, which = 4)

d$q54_p1

##  [1] 3 3 3 3 3 3 4 2 3 3 3 3 3 3 4 4 3 4 3 4 3 3 3 3 3 3 3 4 3 3 3 4 3 4 3 3 3 3
## [39] 3 3 3 4 4 3 3 4 3 3 4 3 3 4 3 3 3 3 4 4 4 3 3 3 4 3 3 3 3 3 3 3 3 2 3 4 4 3
## [77] 3 4 4 3 1 3 3 3 2 3 3 3 3 3 3 3 2 3
## attr(,"format.spss")
## [1] "F8.2"

d_no81$q54_p1

##  [1] 3 3 3 3 3 3 4 2 3 3 3 3 3 3 4 4 3 4 3 4 3 3 3 3 3 3 3 4 3 3 3 4 3 4 3 3 3 3
## [39] 3 3 3 4 4 3 3 4 3 3 4 3 3 4 3 3 3 3 4 4 4 3 3 3 4 3 3 3 3 3 3 3 3 2 3 4 4 3
## [77] 3 4 4 3 3 3 3 2 3 3 3 3 3 3 3 2 3
## attr(,"format.spss")
## [1] "F8.2"

regression model diagnostics

Alejandra Garcia Isaza

2022-07-19

Normality assumption: outcome

linearity

outliers

linearity

outliers

linearity

outliers

linearity

plots

outliers

linearity

outliers

linearity

plots

outliers

linearity

outliers

plots

outliers

plots

outliers

plots

outliers

outliers

outliers

plots

outliers

outliers

plots

outliers